Exotic Derivatives Trading

October 9, 2009

PRDC’s – The game of Long dated FX

Filed under: Risk Management of Exotic Derivatives — Exotics Trader @ 3:04 pm

Cross-Gamma risks and how it impacts the volatility and interest rate markets?

Here we discuss the risks for the USDJPY pair.

Structure is a strip of ITM and OTM (because of forward trading at discount) calls, with issuer having an option to call back the note at every coupon date. The issuer callability feature is synonymous to a knock out feature, since the issuer calls back the note when coupons paid exceed the (Libor received + the value of callability option). So in essence it resembles a KO call type payoff and exhibits similar risks (especially vega)

FX Vega

Seller is short skew because of the callable feature.

The expected maturity of the product changes with changes in volatility, spot and basis (JPY – USD interest rate). An increase in spot, volatility or basis will reduce the tenure since the Moneyness of the option and subsequently chances of issuer calling it back increases.

As spot increases, trader gets longer short term vega. As spot decreases trader gets short long term vega. Later can be a problem because of two reasons

  • Long term vega is illiquid
  • When spot decreases, there is dearth of vega sellers (Everyone rushes to buy protection)

Long term smile is determined by supply demand which might not respond to the dynamics of the FX spot. This poses significant problems in modeling it.

Cross Gamma FX, Interest rate

Issuer is receiving a stream of JPY Libor. An increase in spot decreases the expected maturity and hence traders needs to buyback the long term libor and sell the short term ones. Given the size of the PRDC market, this causes curve steepening and vice-versa when spot decreases.

Clearly the trader is short FX spot, JPY basis (Long term rate – Short term rate) correlation.

Long dated options – Volatility of the forward

When pricing long dated options, one needs to take into account the volatility of the forward which in turn depends on

  • Volatility of the spot
  • and correlation between the spot and the basis (JPY – USD) * Recall the basic no arbitrage equation relating forward with spot and interest rates.

Clearly an increase in correlation will increase the volatility of the forward and hence increase the price of those long term OTM calls.



  1. Wow, great post, thanks. I have asked around quite a bit concerning these, and have received very few good descriptions. Feel free to go more into the pricing of these things… Nice post.

    Comment by Jack — October 14, 2009 @ 3:19 am | Reply

    • Jack, Pricing should not be tough when one can intuitively understand the risks. Please drop me an email at exotics.trader@gmail.com in case you have specific questions.

      What do you do for living ?


      Comment by Exotics Trader — October 14, 2009 @ 4:20 am | Reply

    • Great post, as always. Very interesting.

      Comment by ohhynot — October 14, 2009 @ 9:50 pm | Reply

  2. Sorry, a bit new to this, but how does the callable feature make the seller short skew?

    Comment by mshellie — October 14, 2009 @ 3:23 am | Reply

    • Quick question on this:

      “since the issuer calls back the note when coupons paid exceed the (Libor received + the value of callability option)”

      What do you mean Libor received… ? I understand that eventually, as USDJPY rises, the note will be ITM, and the issuer will call it, meaning that the duration shortens as USDJPY increases. But I don’t see why we are receiving Libor?

      Comment by mdfl — November 28, 2009 @ 10:49 pm | Reply

      • When do you call back the note ? How much ITM ?
        You get my point ? (Its a note, hence the trader is recieving Libor)

        Comment by Nikit Kothari — January 2, 2010 @ 5:00 am

    • If you sell a european binary you are short the skew, hence the skew exposure in this.
      Also if something is autocallable there is a discontinuity according to whether the autocall level is breached. Discontuity = digital behaviour = skew

      Comment by Andy — December 15, 2009 @ 8:42 am | Reply

  3. So how are these products typically hedged? I suppose with 2/10s swap rates in JPY, in USD, and then by buying and selling long mat. FX options? Can you give an example of how this would be hedged?

    Comment by Matt Lyons — October 29, 2009 @ 12:00 am | Reply

  4. Nice post. I’m a trader of these. One thing of interest is how standard modeling assumptions often fail for markets that are completely driven by PRDCs – every dealer is the same way in those markets (e.g. long date FX skew) and thus those markets tend to move in jumps – no banks that I know of uses any sort of jump diffusion model.

    Comment by PRDC trader — December 26, 2009 @ 1:46 pm | Reply

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